News: I may have just found a really complicated but "explicit" or "non-recursive" formula for the solutions of a general recurrence sequence of the form
\( a_1 = r_{1, 1} \),
\( a_n = \sum_{m=1}^{n-1} r_{n, m} a_m \)
which these Schroder function coefficient equations belong to.
It's not "nice", though, but it looks to work (no proof yet as it was found by pattern examination). If you want details, just ask. But at least it seems to show that an explicit formula exists, so that there may perhaps be a simpler, more "elegant" one.
\( a_1 = r_{1, 1} \),
\( a_n = \sum_{m=1}^{n-1} r_{n, m} a_m \)
which these Schroder function coefficient equations belong to.
It's not "nice", though, but it looks to work (no proof yet as it was found by pattern examination). If you want details, just ask. But at least it seems to show that an explicit formula exists, so that there may perhaps be a simpler, more "elegant" one.
